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Limit of series - Factorial example
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Factorial Example\n",
"\n",
"$x\\nearrow1$ で\n",
"$$\n",
"x^{0!}-x^{1!}+x^{2!}-x^{3!}+x^{4!}-x^{5!}+\\cdots \\to\\;???\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# using PyPlot package to plot graphs\n",
"\n",
"using PyPlot"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"21-element Array{Float64,1}:\n",
" 0.999999 \n",
" -0.999999 \n",
" 0.999998 \n",
" -0.999994 \n",
" 0.999976 \n",
" -0.99988 \n",
" 0.99928 \n",
" -0.994973 \n",
" 0.960482 \n",
" -0.69567 \n",
" 0.026548 \n",
" -4.61685e-18 \n",
" 9.37874e-209\n",
" -0.0 \n",
" 0.0 \n",
" -0.0 \n",
" 0.0 \n",
" -0.0 \n",
" 0.0 \n",
" -0.0 \n",
" 0.0 "
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x=0.999999\n",
"[(-1)^k*x^(factorial(k)) for k in 0:20]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\"\\$f(x)=x^{0!}-x^{1!}+x^{2!}-x^{3!}+x^{4!}-x^{5!}+\\\\cdots\\$\""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"f (generic function with 1 method)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# definition of f(x,n)\n",
"# sum of x^{k!} w.r.t. k = 0..n\n",
"\n",
"series = \"\\$f(x)=x^{0!}-x^{1!}+x^{2!}-x^{3!}+x^{4!}-x^{5!}+\\\\cdots\\$\"\n",
"display(series)\n",
"f(x::Float64, n::Float64) = sum([(-1)^k*x^(factorial(k)) for k in 0:n if 0.0 < abs(x^(factorial(k))) < 1.0])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x0000000027AE1A20>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.text.Text object at 0x000000002F0BC5C0>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# plot f(x) for x = 0 to 1\n",
"\n",
"x = [linspace(0.0,0.999999,1000);]\n",
"plot(x, f.(x, 30.0))\n",
"title(series, fontsize=16)\n",
"xlabel(\"\\$x\\$\", fontsize=12)\n",
"ylabel(\"\\$f(x)\\$\", fontsize=12)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"20×2 Array{Float64,2}:\n",
" 0.999 0.573512\n",
" 0.99905 0.585146\n",
" 0.9991 0.596871\n",
" 0.99915 0.60856 \n",
" 0.9992 0.62004 \n",
" 0.99925 0.631086\n",
" 0.9993 0.641399\n",
" 0.99935 0.650589\n",
" 0.9994 0.658146\n",
" 0.99945 0.663409\n",
" 0.9995 0.665519\n",
" 0.99955 0.663364\n",
" 0.9996 0.655502\n",
" 0.99965 0.640075\n",
" 0.9997 0.614685\n",
" 0.99975 0.576258\n",
" 0.9998 0.521005\n",
" 0.99985 0.445314\n",
" 0.9999 0.3541 \n",
" 0.99995 0.325563"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# oscillation?\n",
"\n",
"x=[0.99900:0.00005:0.99995;]\n",
"[x'; f.(x, 30.)']'"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000002F102BE0>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.text.Text object at 0x00000000336892E8>"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# near x=1\n",
"\n",
"x = [linspace(0.999,0.999999,30);]\n",
"plot(x, f.(x, 40.))\n",
"#title(series, fontsize=16)\n",
"xlabel(\"\\$x\\$\", fontsize=12)\n",
"ylabel(\"\\$f(x)\\$\", fontsize=12)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000002FC6E7F0>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.text.Text object at 0x0000000033889A90>"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# log scale plot near x=1a\n",
"\n",
"t = [linspace(3,15.5,100);]\n",
"x = 1 .- 10.^(-t)\n",
"plot(t, f.(x, 40.))\n",
"title(\"log scale plot\", fontsize=16)\n",
"xlabel(\"\\$t=-\\\\log_{10}(1-x)\\$\", fontsize=12)\n",
"ylabel(\"\\$f(x)=f(1-10^{-t})\\$\", fontsize=12)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x000000003393E9B0>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.text.Text object at 0x0000000033E320B8>"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t = [linspace(3,20,100);]\n",
"x = 1 .- 10.^(-t)\n",
"plot(t, f.(x, 30.))\n",
"title(\"log scale plot\", fontsize=16)\n",
"xlabel(\"\\$t=-\\\\log_{10}(1-x)\\$\", fontsize=12)\n",
"ylabel(\"\\$f(x)=f(1-10^{-t})\\$\", fontsize=12)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"_draft": {
"nbviewer_url": "https://gist.github.com/f534862d95fd0a37a0562398150fe3cb"
},
"gist": {
"data": {
"description": "Julia/Limit of series - Factorial example.ipynb",
"public": true
},
"id": "f534862d95fd0a37a0562398150fe3cb"
},
"kernelspec": {
"display_name": "Julia 0.6.0",
"language": "julia",
"name": "julia-0.6"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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